I had the feeling my post may be too obscure :) And I have no idea how I might have given rise to the suspicion that I oppose the all-shining multiculturalism.
What I was trying to say is that English culture is very seductive; though it may not necessarily be world-wide as in universalistic, it certainly is penetrating. If you wish, a local culture so powerful that it had become universal. How many trends have come from the UK, and how many people (and how many teenagers), in how many places and how many periods of time had it affected? And through language it has become even more accessible and penetrating. In short, one of the most loved and well known and respected countries in the world. From this points of view, it may be a little redundant to ask what attracts others to the UK.
As for me, what counts the most is the place and the people themselves. Your overall country branding, if I may say so, has irrevocably gotten to me. I'm still in Romania, but plan to come here in a few months' time. What I expect is not necessarily an increase in life quality (though it will be) but in life style. Those that earnestly say they are here just for the jobs and the money should think again. Would they move to, say Saudi Arabia, if they'd be paid better there? To get a little academic, a recent UN study has come to the conclusion that the main driver for worldwide migration is not economics but to escape an irksome (their exact word) local culture. And I know most of the people here can relate to that. I don't mind being poor in the UK as opposed to being middle-class home (and I'm not talking about money here). It's about being part of a better (avoid the word "superior") culture, even as an outsider.
I'm sorry if my answer may border on the wrong side of political correctness, indeed it has become excessive. So, what attracts me and many others to the UK: the answer is you, and the great job that you have done.
(Note: I don't intend to criticise my native culture by this, so please don't jump all over me. I'm just saying it is a mediocre, average one, like the majority, as opposed to a "better" one. Shoot away :)